CHAP. I.] NATURE AND DESIGN OF THIS WORK. 9 



ber of symbols representing terms or elements in Logic may be 

 eliminated ; and from any number of equations representing pro- 

 positions, one or any other number of symbols of this kind may 

 be eliminated in a similar manner. For such elimination there 

 exists one general process applicable to all cases. This is one of 

 the many remarkable consequences of that distinguishing law of 

 the symbols of Logic, to which attention has been already 

 directed. 



2ndly . It should be within the province of a general method 

 in Logic to express the final relation among the elements of the 

 conclusion by any admissible kind of proposition, or in any se- 

 lected order of terms. Among varieties of kind we may reckon 

 those which logicians have designated by the terms categorical, 

 hypothetical, disjunctive, &c. To a choice or selection in the 

 order of the terms, we may refer whatsoever is dependent upon 

 the appearance of particular elements in the subject or in the 

 predicate, in the antecedent or in the consequent, of that propo- 

 sition which forms the " conclusion." But waiving the language 

 of the schools, let us consider what really distinct species of 

 problems may present themselves to our notice. We have seen 

 that the elements of the final or inferred relation may either be 

 things or propositions. Suppose the former case ; then it might 

 be required to deduce from the premises a definition or description 

 of some one thing, or class of things, constituting an element of 

 the conclusion in terms of the other things involved in it. Or 

 we might form the conception of some thing or class of things, 

 involving more than one of the elements of the conclusion, and 

 require its expression in terms of the other elements. Again, 

 suppose the elements retained in the conclusion to be propo- 

 sitions, we might desire to ascertain such points as the following, 

 viz., Whether, in virtue of the premises, any of those propo- 

 sitions, taken singly, are true or false ? Whether particular 

 combinations of them are true or false ? Whether, assuming a 

 particular proposition to be true, any consequences will follow, 

 and if so, what consequences, with respect to the other propo- 

 sitions ? Whether any particular condition being assumed with 

 reference to certain of the propositions, any consequences, and 

 what consequences, will follow with respect to the others ? and 



